I want to classify the input as one of 3 possibilities. Is it better to use 3 networks with one output each or 1 network with 3 outputs?
(i.e. 3 networks that output 0 or 1 or 1 network that outputs a one hot vector of length 3 [1,0,0]
Does the answer change depending on how complex the incoming data is to classify?
At what amount of outputs does it make sense to partition the networks (if ever)? For example, if I want to classify into 20 groups, does it make a difference?
I would say it would make more sense to use a single network with multiple outputs.
The main reason is that hidden layers (I'm assuming you'll have at least one hidden layer) can be interpreted as transforming the data from the original space (feature space) into a different space that is more suitable for the task (classification in your case). For example, when training a network to recognize faces from raw pixels, it might use a hidden layer to first detect simple shapes such as small lines based on pixels, then use another hidden layer to detect simple shapes such as eyes/noses based on the lines from the first layer, etc. (it may not be entirely as ''clean'' as this, but this is an easy-to-understand example).
Such a transformation that a network can learn is typically useful for the classification task, regardless of what class the specific example has. For example, it is useful to be able to detect eyes in images regardless of whether or not the actual image contains a face; if you do indeed detect two eyes, you can classify it as a face, and otherwise you classify it as not being a face. In both cases, you were looking for eyes.
So, by splitting up into multiple networks, you may end up learning quite similar patterns in all networks anyway. Then you might as well have saved yourself the computational effort and just learned it once.
Another disadvantage of splitting up into multiple networks would be that you would probably cause your dataset to become imbalanced (or more imbalanced if it already is imbalanced). Suppose you have three classes, with exactly 1/3 of the dataset belonging to each class. If you use three networks for three binary classification tasks, you suddenly always have 1/3 ''1'' classes and 2/3 ''0'' classes. A network may then become biased towards predicting 0s everywhere, since those are the majority classes in each of the three separate problems.
Note that this is all based on my intuition; the best solution if you have time would be to simply try both approaches and test! I don't think I have ever seen someone using multiple networks for a single classification task in practice though, so if you only have time for one approach I'd recommend going for a single network.
I think the only case where it would really make sense to use multiple networks would be if you actually want to predict multiple unrelated values (or at least values that are not strongly related). For example, if, given images, you want to 1) predict whether or not there is a dog on the image, and 2) whether it is a photograph or a painting. Then it may be better to use two networks with two outputs each, instead of a single network with four outputs.
